Btw, the answer you were alluding to as not being legit, absolutely is legit. The plain fact is that a CPU upgrade will NOT yield a sizeable performance boost in most games unless either you have a very weak CPU and/or a very powerful GPU. It is one of the benefits of this forum that people give it to you as they see it, which is not necessarily what you wanna hear or are expecting!
Of course there are many reasons why you might want to upgrade and if you do, there's no better choice than an I5 3570k. Just don't expect any really substantial performance boost in games vs what you already have. For a start, it will have no impact whatsoever on what resolution you can run it at or the AA/other eye candy you can turn on - those are only about the GPU and have nothing whatsoever to do with CPU.
Yes, there are some games where you will get a measurable performance boost - but the real question is, is measurable the same as practical? A faster CPU than yours would reduce (but not eliminate) the odd stutter or slowdown, but the difference will certainly not be huge and my guess is you'll be left feeling disappointed in the return for your money. Skyrim would benefit to some extent in the more complex scenes (e.g. in cities) but it also depends on whether it's really the CPU that's holding back performance. The same scenes can also be quite taxing on the GPU as well. The GPU intensive games would see no benefit whatsoever.
With a "good enough" CPU (such as yours), you will almost always get a better return by upgrading your GPU.
Actually to be honest I've long pursued the ultimate goal of the gaming rig capable of running anything on max settings with no hint of stutter ever, anywhere. After investing in a second GTX 680 I have concluded that it's a completely impossible dream. It's really a question of what level of performance you find acceptable, and if you're not getting it, investing in the part that yields the biggest impact. In your case I sincerely doubt it's the CPU.
By the way, overclocking is really easy, free, and well worth a try.